For a given input value $u$, the function $g$ outputs a value $v$ to satisfy the following equation. $-12u+3=8v+1$ Write a formula for $g(u)$ in terms of $u$. $g(u)=$
Solution: $g(u)$ expresses $v$ as a function of $u$. To arrive at a correct formula, all we have to do is solve the equation for $v$. $ \begin{aligned}-12u+3&=8v+1\\\\ -12u+2&=8v\\\\ \dfrac{-12u}{8}+\dfrac{2}{8}&=v\\\\ -\dfrac{3}{2}u+\dfrac{1}{4}&=v\end{aligned}$ Therefore, this formula expresses $v$ as a function of $u$ : $ g(u)=-\dfrac{3}{2}u+\dfrac{1}{4}$